# Relationship between refraction and speed of light

### Refractive index - Wikipedia

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as. n = c v, {\displaystyle n={\frac {c}{v}},} n={\frac {c}{v}},. where c is the speed of light in vacuum and v is the phase velocity of light in . For visible light most transparent media have refractive. Light travels as waves, with the wavefronts perpendicular to the direction of motion. As we saw in the Review page, the wave's speed v is related to both the of index of refraction, we find a relationship between the wavelength = v/f in a. According to the formula, the index of refraction is the relation between the speed of light in a vacuum and the speed of light in a substance. But what is refraction.

This can occur close to resonance frequenciesfor absorbing media, in plasmasand for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 exceptions close to some resonance frequencies. Since the refractive index of the ionosphere a plasmais less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" see Geometric optics allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.

See also Radio Propagation and Skywave. Negative index metamaterials A split-ring resonator array arranged to produce a negative index of refraction for microwaves Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values. The resulting negative refraction i. Ewald—Oseen extinction theorem At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom primarily the electrons proportional to the electric susceptibility of the medium.

Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility. As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency. The light wave traveling in the medium is the macroscopic superposition sum of all such contributions in the material: This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity.

Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies see scattering. Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities: This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.

This is called "anomalous refraction", and is observed close to absorption lines typically in infrared spectrawith X-rays in ordinary materials, and with radio waves in Earth's ionosphere. It corresponds to a permittivity less than 1, which causes the refractive index to be also less than unity and the phase velocity of light greater than the speed of light in vacuum c note that the signal velocity is still less than c, as discussed above.

If the response is sufficiently strong and out-of-phase, the result is a negative value of permittivity and imaginary index of refraction, as observed in metals or plasma. This is light absorption in opaque materials and corresponds to an imaginary refractive index.

### Wavelength and the Index of Refraction

If the electrons emit a light wave which is in phase with the light wave shaking them, it will amplify the light wave. When the wave impinges upon a particle of matter, the energy is absorbed and sets electrons within the atoms into vibrational motion.

If the frequency of the electromagnetic wave does not match the resonant frequency of vibration of the electronthen the energy is reemitted in the form of an electromagnetic wave.

This new electromagnetic wave has the same frequency as the original wave and it too will travel at a speed of c through the empty space between atoms.

### ddttrh.info: Light & Optics: Refraction

The newly emitted light wave continues to move through the interatomic space until it impinges upon a neighboring particle. The energy is absorbed by this new particle and sets the electrons of its atoms into vibration motion. And once more, if there is no match between the frequency of the electromagnetic wave and the resonant frequency of the electron, the energy is reemitted in the form of a new electromagnetic wave.

The cycle of absorption and reemission continues as the energy is transported from particle to particle through the bulk of a medium. Every photon bundle of electromagnetic energy travels between the interatomic void at a speed of c; yet time delay involved in the process of being absorbed and reemitted by the atoms of the material lowers the net speed of transport from one end of the medium to the other.

## Refractive index

Optical Density and the Index of Refraction Like any wave, the speed of a light wave is dependent upon the properties of the medium. In the case of an electromagnetic wave, the speed of the wave depends upon the optical density of that material.

The optical density of a medium is not the same as its physical density. The optical density of a material relates to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance.

## Optical Density and Light Speed

The more optically dense that a material is, the slower that a wave will move through the material. One indicator of the optical density of a material is the index of refraction value of the material. Index of refraction values represented by the symbol n are numerical index values that are expressed relative to the speed of light in a vacuum.

The index of refraction value of a material is a number that indicates the number of times slower that a light wave would be in that material than it is in a vacuum.